Final answer:
The statement is true for a constant function on an interval, as both the right and left Riemann sums will give the exact area under the curve, which is calculated as the product of the constant function value and the length of the interval.
Step-by-step explanation:
The statement is true: If f is a constant function on the interval [a, b], then the right and left Riemann sums give the exact value of ∫ab f(x) dx, for any positive integer n. This is because a constant function has the same value at each point in its domain. Let's denote the constant value of the function as c. Due to the uniformity of the function's value across the interval, partitioning the interval into n subintervals and using either right or left endpoints to evaluate the function for Riemann sums will result in the same height c for each rectangle of the partition. Multiplying the value c by the width of each subinterval and summing over all n rectangles gives us the product c(b - a), which is precisely the definite integral of f over the interval [a, b].
For example, if f(x) = k for some constant k over the interval [0, 20], then the integral of f from 0 to 20 is simply 20k since it represents the area under the curve f(x), which is a rectangle with height k and width 20.